Understanding leverage in Forex trading?

Let’s say I have $1K balance and my broker offers 100:1 leverage so that my buying power is $100K. I buy the Yen for $100K because I predict that Yen will rise in a week or so but I also predict that it will initially fall for like a day or two. So when the Yen falls in the first 2 days, my equity – as I understand it – will be negative. Will the broker close my position if they see that my equity is negative OR can I have this position open for as long as I like and hope for Yen to rise some day?